* The TV show "Hell's Kitchen": It's a reality cooking competition show run by Gordon Ramsay.
* The fictional location "Hell's Kitchen": In literature and folklore, "Hell's Kitchen" often refers to a rough, crowded, and dangerous part of New York City. There's no single person "running" it in this sense.
* A specific restaurant: If you're thinking of a restaurant named "Hell's Kitchen," you'd need to provide more information about the location to know who runs it.
Could you please clarify your question?